Existence and Ergodicity for the Two-Dimensional Stochastic Magneto-Hydrodynamics Equations

The paper proves the existence of solutions to the magneto-hydrodynamics equations driven by random exterior forcing terms both in the velocity and in the magnetic field. The existence and uniqueness of an invariant measure is also obtained via coupling methods.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Practical aspects of the uncertainty and traceability of spectrochemical measurement results by electrothermal atomic absorption spectrometry

The determination of trace elements concentration in water by electrothermal atomic absorption spectrometry (ETAAS) is a common and well established technique in many chemical testing laboratories. However, the evaluation of measurement uncertainty results is not systematically implemented. The paper presents an easy step-by-step example leading to the evaluation of the combined standard uncertainty of copper determination in water using ETAAS. The major contributors to the overall measurement uncertainty are identified due to amount of copper in water sample that mainly depends on the absorbance measurements, due to certified reference material and due to auto-sampler volume measurements. The practical aspects how the traceability of copper concentration in water can be established and demonstrated are also pointed out.     

Semilinear integro-differential equations in Hilbert space

Existence, uniqueness and asymptotic behavior of solutions to integro-differential equations involving monotone operators are discussed.     

Robust Contour Tracking Model Using a Variational Level-Set Algorithm

In this work, we provide a novel variational level-set based object contour tracking approach. Thus, a mathematically rigorous variant of the Chan-Vese algorithm for image segmentation via geometric active contour model is proposed here. With respect to the original contour detection algorithm, the level set function ?(t) defining the evolving contour S _t  = {x; ?(t, x) = 0} is iteratively computed from a nonlinear parabolic boundary value problem that is well posed in the space of functions with bounded variations. We provide a robust mathematical justification of the proposed level-set model.     

Adaptive efficient estimation for generalized semi-Markov big data models

Annals of the Institute of Statistical Mathematics - In this paper we study generalized semi-Markov high dimension regression models in continuous time, observed at fixed discrete time moments. The...     

Exact controllability for the magnetohydrodynamic equations

We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a fixed‐point argument. The treatment of the reduced problem relies on two Carleman‐type inequalities for the backward adjoint system. © 2003 Wiley Periodicals, Inc.     

The obtaining of NiCr2O4 nanoparticles by unconventional synthesis methods

This paper presents a study regarding the obtaining of NiCr₂O₄ by two new unconventional synthesis methods: (i) the first method is based on the formation of Cr(III) and Ni(II) carboxylate-type precursors in the redox reaction between the nitrate ion and 1,3-propanediol. The thermal decomposition of these complex combinations, at ~300 °C, leads to an oxide mixture of Cr₂O_3+x and NiO, with advanced homogeneity, small particles and high reactivity. On heating this mixture at 500 °C, Cr₂O₃ reacts with NiO to form NiCr₂O₄, which was evidenced by FT-IR and X-ray diffractometry (XRD) analysis; (ii) the second method starts from a mechanical mixture of (NH₄)₂Cr₂O₇ and Ni(NO₃)₂·6H₂O. On heating this mixture, a violent decomposition at 240 °C with formation of an oxides mixture (Cr₂O₃ + CrO₃) and NiO takes place. On thermal treatment up to 500 °C, an intermediary phase NiCrO₄ is formed, which by decomposition at ~700 °C leads to NiCr₂O₄, evidenced by FT-IR and XRD analysis. NiCr₂O₄ is formed, in both cases, starting with a temperature higher than 400 °C, when the non-stoichiometric chromium oxide (Cr₂O_3+x ) loses the oxygen excess and turns to stoichiometric chromium oxide (Cr₂O₃), which further reacts with NiO.